IEICE TRANSACTIONS on Fundamentals
Correlation Distributions between an m-Sequence and Its Niho Decimation Sequences of Short Period
Summary :
Let d=2pm-1 be the Niho decimation over $mathbb{F}_{p^{2m}}$ satisfying $gcd(d,p^{2m}-1)=3$, where m is an odd positive integer and p is a prime with p ≡ 2(mod 3). The cross-correlation function between the p-ary m-sequence of period p2m-1 and its every d-decimation sequence with short period $ rac{p^{2m}-1}{3}$ is investigated. It is proved that for each d-decimation sequence, the cross-correlation function takes four values and the corresponding correlation distribution is completely determined. This extends the results of Niho and Helleseth for the case gcd(d, p2m-1)=1.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E102-A No.2 pp.450-457
- Publication Date
- 2019/02/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E102.A.450
- Type of Manuscript
- PAPER
- Category
- Information Theory
Authors
Yongbo XIA
South-Central University for Nationalities
Shiyuan HE
South-Central University for Nationalities
Shaoping CHEN
South-Central University for Nationalities
Keyword
Latest Issue
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Yongbo XIA, Shiyuan HE, Shaoping CHEN, "Correlation Distributions between an m-Sequence and Its Niho Decimation Sequences of Short Period" in IEICE TRANSACTIONS on Fundamentals,
vol. E102-A, no. 2, pp. 450-457, February 2019, doi: 10.1587/transfun.E102.A.450.
Abstract: Let d=2pm-1 be the Niho decimation over $mathbb{F}_{p^{2m}}$ satisfying $gcd(d,p^{2m}-1)=3$, where m is an odd positive integer and p is a prime with p ≡ 2(mod 3). The cross-correlation function between the p-ary m-sequence of period p2m-1 and its every d-decimation sequence with short period $ rac{p^{2m}-1}{3}$ is investigated. It is proved that for each d-decimation sequence, the cross-correlation function takes four values and the corresponding correlation distribution is completely determined. This extends the results of Niho and Helleseth for the case gcd(d, p2m-1)=1.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E102.A.450/_p
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@ARTICLE{e102-a_2_450,
author={Yongbo XIA, Shiyuan HE, Shaoping CHEN, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Correlation Distributions between an m-Sequence and Its Niho Decimation Sequences of Short Period},
year={2019},
volume={E102-A},
number={2},
pages={450-457},
abstract={Let d=2pm-1 be the Niho decimation over $mathbb{F}_{p^{2m}}$ satisfying $gcd(d,p^{2m}-1)=3$, where m is an odd positive integer and p is a prime with p ≡ 2(mod 3). The cross-correlation function between the p-ary m-sequence of period p2m-1 and its every d-decimation sequence with short period $ rac{p^{2m}-1}{3}$ is investigated. It is proved that for each d-decimation sequence, the cross-correlation function takes four values and the corresponding correlation distribution is completely determined. This extends the results of Niho and Helleseth for the case gcd(d, p2m-1)=1.},
keywords={},
doi={10.1587/transfun.E102.A.450},
ISSN={1745-1337},
month={February},}
Copy
TY - JOUR
TI - Correlation Distributions between an m-Sequence and Its Niho Decimation Sequences of Short Period
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 450
EP - 457
AU - Yongbo XIA
AU - Shiyuan HE
AU - Shaoping CHEN
PY - 2019
DO - 10.1587/transfun.E102.A.450
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E102-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 2019
AB - Let d=2pm-1 be the Niho decimation over $mathbb{F}_{p^{2m}}$ satisfying $gcd(d,p^{2m}-1)=3$, where m is an odd positive integer and p is a prime with p ≡ 2(mod 3). The cross-correlation function between the p-ary m-sequence of period p2m-1 and its every d-decimation sequence with short period $ rac{p^{2m}-1}{3}$ is investigated. It is proved that for each d-decimation sequence, the cross-correlation function takes four values and the corresponding correlation distribution is completely determined. This extends the results of Niho and Helleseth for the case gcd(d, p2m-1)=1.
ER -
English
